How to solve an Improper Integral of Type 2?

[cmab]

I've posted on Homeworks one of the number I did not understand. However, I would like to know the steps to calculate an improper integral of type 2. The type 2 is the one from constant a to constat b, not the one with inifnite.

Please tell me the steps the accomplish it.

I know that I'm supposed to set the limits, then put it in the integral form, than FTC it. But, I'm not sure.

 

[limitapproaches0]

Could you give example so I could understand question a little better.

 

[cmab]

Could you give example so I could understand question a little better.

Let's say something like [int a=0 b=2] 1/(x-1)^(1/3) dx

 

[dextercioby]

Use the theorem of addition

$$\int_{0}^{2} f(x) \ dx=\int_{0}^{1} f(x) \ dx+\int_{1}^{2} f(x) \ dx$$

You have to integrate & compute 2 limits...

Daniel.

 

[cmab]

Use the theorem of addition

$$\int_{0}^{2} f(x) \ dx=\int_{0}^{1} f(x) \ dx+\int_{1}^{2} f(x) \ dx$$

You have to integrate & compute 2 limits...

Daniel.

The limits would be 1+ and 1- right ?

 

[dextercioby]

It should be

$$\lim_{a\nearrow 1}\int_{1}^{a} f(x) \ dx$$

$$\lim_{b\searrow 1}\int_{b}^{2} f(x) \ dx$$


Daniel.